On Discrete Symmetries and Torsion Homology in F-Theory

We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a $\mathbb Z_2$ symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a $\mathbb Z_2$ gauge symmetry. We show that the resulting five-dimensional theories do not have a $\mathbb Z_2$ symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit discrete torsion. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a $\mathbb Z_2$ symmetry in five dimensions and, accordingly, we find explicitly an associated discrete torsion. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.Comment: 12 pages in 2-column style, 4 figures; v2: references adde

Abstracts of unpublished theses on the gifted child found in the School of Education Library at Boston University which were not included in the Gaffney thesis of 1958

Thesis (Ed.M.)--Boston UniversityAndrews, Charles Herbert. "A Survey of Curriculum Materials of Value for the Teaching of Gifted Elementary School Children in the Language Arts Area." Unpublished Ed. M. Thesis, Boston University School of Education, 1957. Problem. To determine the curriculum materials which should be included in an elementary school classroom devoted to the maximal effective teaching of gifted children in the language arts area. [TRUNCATED

Discontinuous Tradition of Sentencing Discretion: Koon\u27s Failure to Recognize the Reshaping of Judicial Discretion under the Guidelines, The

Can a judge exercise discretion and follow the law? Some think it impossible, seeing discretion as the opposite of law. Others have harmonized the two ideas, viewing discretion as the exercise of judgment according to and within the bounds of the law. Those who decry judicial discretion urge legislatures to enact more specific laws and leave less room for the vice of inconsistent results. Those who defend discretion would channel it to achieve the virtue of individualized justice. The tension between individualization and uniformity in the law is often unnecessarily heightened by an inadequate analysis of judicial discretion. The exercise of judicial discretion in federal criminal sentencing exemplifies the problems arising from those inadequate analyses. The Sentencing Reform Act of 1984 ( SRA ) dramatically altered federal criminal sentencing for the express purpose of controlling judicial discretion. Judges were once free to impose any sentence from probation to the statutory maximum and were not subject to appellate review regarding the length of that sentence. However, they are now bound by the Sentencing Guidelines 7 and subject to appellate review of the sentences they impose. Despite this dramatic change, or perhaps because of it, the Supreme Court has used the breadth and uncertainty of the concept of discretion to paper over the fundamental reallocation of sentencing power in an effort to buttress the limited authority judges retain to individualize sentences

Outlier Detection from Network Data with Subnetwork Interpretation

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why the network is exceptional, expressed in the form of subnetwork, is also equally important. In this paper, we develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that mostly discriminate it from nearby regular samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery and we show that it converges to a global optimum. Evaluation on various real-world network datasets demonstrates that our algorithm not only outperforms baselines in both network and high dimensional setting, but also discovers highly relevant and interpretable local subnetworks, further enhancing our understanding of anomalous networks

Fisher Hartwig determinants, conformal field theory and universality in generalised XX models

We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups. We show how these models correspond to translation invariant models on an infinite or semi-infinite chain, which in the simplest case reduce to the familiar XX model. We give physical context to mathematical results for the entanglement entropy, and calculate the spin-spin correlation functions using the Fisher-Hartwig conjecture. These calculations rigorously demonstrate universality in classes of these models. We show that these are in agreement with field theoretic and renormalization group arguments that we provide

From the voice of a ‘Socratic Gadfly’: a call for more academic activism in the researching of disability in postsecondary education

In this article I use the lens of voices and silences to frame my review of research in the field of disability and postsecondary education. I argue that we need to view research in this field as a necessarily political act that seeks to turn voices of silence into voices of change. Researchers therefore need to re-think their role in order to understand how they can use and direct their political voices. In order to persuade researchers to heed my call for more academic activism I draw on the arguments of Allan (2010) and adopt the role of a ‘socratic gadfly’ to identify six political areas of research where I argue that voices and silences need more critical examination. In discussing these six areas I hope to illuminate the implications for ‘genuinely investigative’ research in the future

Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.Comment: 19 pages, 14 figures, published version with minor change

State Accountability System: Action Guide for Parents and Communities

NCLB requires that each state develop and implement a single, state wide accountability system assuring that each public school district and all public and elementary schools make adequate yearly progress based on the components reviewed in this guide